Introduction to Quantum Theory

Transcription

1 Introduction to Quantum Theory Dr. Russell Herman Physics and Physical Oceanography PHY Quantum Theory - Fall

2 Syllabus Website: Grades Homework 30% Papers 10% 3 Exams 40% Final 20% Required Text: Townsend, J. A Modern Approach to Quantum Mechanics, 2nd Ed., Recommended Text: Susskind, L. Quantum Mechanics, The Theoretical Minimum, Other: Feynman, R. C., The Feynman Lectures on Physics, Vol. III, 1965 and QED: The Strange Theory of Light and Matter, See also - PHY Quantum Theory - Fall

3 The Rise of Classical Physics PHY Quantum Theory - Fall

4 Scientific Deduction Tycho Brahe ( ) Johannes Kepler ( ) Galileo Galilei ( ) PHY Quantum Theory - Fall

5 The Clockwork Universe Sir Isaac Newton ( ) Principia (1687) Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) Laws of Motion Law of Gravitation Kepler's Laws Explained Calculus... space is absolute... dp/dt = F Determinism - Given F, predict x and v Unification... the force responsible for bodies falling on the Earth is the same as that causing the moon to follow its orbit. PHY Quantum Theory - Fall

6 Re-formulations J. Bernoulli ( ) Euler ( ) Variational Calculus D Alembert ( ) Lagrange ( ) Lagrangian Mechanics Hamilton ( ) Hamiltonian Mechanics Define the action t, for. 2 S = L dt L = T V t1 Require: δ S = 0. Then, d L L = 0. dt x x Principles Fermat s d Alembert s Hamilton s least time virtual work least action PHY Quantum Theory - Fall

7 Hamilton's Formulation Phase Space (q=x, p= m dx/dt), Initial (p,q) + 2 nd Law => Motion for all t Ex: Free particle, p = const Harmonic Oscillator, Energy Conservation E=const E 2 p 1 = + 2m 2 kq 2 Hamiltonian H(p,q) = T(p) + V(q) Hamilton's Eqns <=> Newton's Laws dq dt = H ( q, p) p dp H ( q, p) = dt q PHY Quantum Theory - Fall

8 Electricity and Magnetism Magnetism Lode stones Compasses William Gilbert ( ) Thomas Browne ( ) Benjamin Franklin ( ) Luigi Galvani ( ) Alessandro Volta ( ) PHY Quantum Theory - Fall

9 Electromagnetism André-Marie Ampère, ( ) Hans Oersted ( ) current deflects compass needles Georg Simon Ohm ( ) Joseph Henry ( ) electromagnetic induction, first motor, telegraph Michael Faraday ( ) electrolysis, motors, induction coils,... PHY Quantum Theory - Fall

10 Electromagnetic Waves James Clerk Maxwell ( ) - Theory of electromagnetism. - Predicted the electromagnetic waves. - Electromagnetic waves travel at c = 299,792,458 m/s = 186,000 mi/s Heinrich Hertz ( ) - sent the first radio waves (1888) What is the medium? Luminiferous Aether Michelson-Morley (1887) - could not detect it. PHY Quantum Theory - Fall

11 Maxwell's Equations PHY 444 -Quantum Theory - Fall

12 Gaussian Units PHY Quantum Theory - Fall 2018

13 EM WAVES 2 1 E c 2 2 t = 2 E What are waves? Characteristics Wavelength, Frequency, Wavespeed Behavior Superposition, Interference. Diffraction PHY Quantum Theory - Fall

14 Spectroscopy Ionized gas gives off radiation Johann Balmer 1885 Spectral Lines: Hydrogen 410, 434, 486, 656 nm Empirical Formula: λ = R (1/4 1/n 2 ) Predicted 5th-7th lines Lyman and Paschen Series PHY Quantum Theory - Fall

15 Laws of Thermodynamics James Joule ( ) Mechanical Equivalent of Heat Engines: Watt, Carnot, Kelvin, Clausius, Carnot Laws of Thermodynamics 1. Adding heat energy or doing work on a body increases internal energy. (Energy conservation) 2. A body will not spontaneously get hotter. (Entropy and the Arrow of Time) Joseph Stefan ( ) and Ludwig Boltzmann ( ) Heated bodies Radiate - Stefan-Boltzmann Law Radiation from blackbody proportional to T 4. P = eσ AT 4 Maxwell-Boltzmann Statistical Mechanics Bah Humbug! PHY 444 -Quantum Theory - Fall

16 H ψ = i t ψ 8π G G +Λ g = T c This is not your father's physics µν µν 4 µν i γ µ µ mc ψ = 0 x p 2 PHY 444 -Quantum Theory - Fall

17 Physics Revolutions William Thomson, ( ) 1st Baron Kelvin (Lord Kelvin) There is nothing new to be discovered in physics now. All that remains is more and more precise measurement Wilhelm Röntgen discovers X-rays. NP Henri Becquerel discovers radioactivity NP Marie and Pierre Curie separate radioactive elements 1897 Joseph (J.J.) Thomson measures electron, NP 1906 NP 1903 plum-pudding model of atom PHY 444 -Quantum Theory - Fall

18 Radioactivity and the Atom J.J. Thomson discovers the electron NP Marie and Pierre Curie discover the first radioactive elements: radium and polonium NP Ernest Rutherford divided radiation into alpha and beta rays NP Pierre Curie observes gamma rays Ernest Rutherford discovers the atomic nucleus Niels Bohr introduces the first atomic model, the mini solar system. NP Hans Geiger invents counter for measuring radioactivity Ernest Rutherford discovered and named the proton James Chadwick discovers the neutron. NP 1935 PHY 444 -Quantum Theory - Fall

19 Blackbody Spectrum Blackbody - a theoretical object that absorbs 100% of the radiation that hits it. Wien's Law (1896) NP 1911 and Rayleigh NP Jeans Law (1900) Ultraviolet Catastrophe... when you turn on your toaster, you are instantly fried by a massive gamma ray burst, since your little blackbody toaster should emit infinite energy at the shortest wavelengths. PHY 444 -Quantum Theory - Fall

20 Quantum Theory Max Planck NP 1918 (Karl Ernst Ludwig Max Planck ) oscillators can only vibrate at discrete frequencies: E n = n(hf), n =1,2,3... Thus, the energy difference E = hf, where Planck's constant is given by h = 6.63 x Js PHY 444 -Quantum Theory - Fall

21 Albert Einstein PHY 444 -Quantum Theory - Fall

22 Paradigm Shifts Relativity Space and Time not absolute, not Euclidean Quantum Mechanics Loss of Determinism PHY 444 -Quantum Theory - Fall

23 Bohr's Atom Niels Bohr ( ) Accelerating electrons radiate at specific energies. Are atoms stable? Assume angular momentum is quantized. E n 1 1 = RH m n 2 2 PHY 444 -Quantum Theory - Fall

24 Early History - Quantum Mechanics Planck Explains Blackbody Radiation NP Einstein - the Photoelectric Effect, Photons The Bohr Model for Hydrogen NP 1922 NP Confirmation of photon, Millikan NP Stern-Gerlach Experiment NP Compton NP 1927 Effect X-Ray Scattering 1924 de Broglie NP Particles Behave Like Waves Matrix Mechanics Heisenberg NP 1932, Born NP 1954, Jordan - Pauli Principle NP Wave Mechanics - Schrödinger NP The Uncertainty Principle Heisenberg - Davisson NP 1937 Germer, Thomson NP 1937 Verified debroglie's idea Relativistic Quantum Mechanics - Dirac NP 1933 PHY 444 -Quantum Theory - Fall

25 Stern-Gerlach Experiment Otto Stern ( ) Walther Gerlach ( ) Ag atoms sent through inhomogenous magnetic field. PHY Quantum Theory - Fall

26 Stern-Gerlach Results Test of classical vs quantum theory of angular momentum (L). L=0 or L=1 No splitting for L=0? Uhlenbeck and Goldsmit (1925,1926) proposed intrinsic spin. To explain anomalous Zeeman effect, (the splitting of spectral lines in a magnetic field). PHY Quantum Theory - Fall 2018

27 Stern-Gerlach Particle Path PHY Quantum Theory - Fall 2018

28 Stern-Gerlach Thought Experiments PHY 444 -Quantum Theory - Fall